动态规划——LCS 最大子数组问题

源代码：

#include <stdio.h>
#include <iostream>

using namespace std;

int const N = 100;
int x[N] = { NULL,1,2,3,2,4,1,2 };
int y[N] = { NULL,2,4,3,1,2,1 };
int m = 7;
int n = 6;
static int b[N][N];            //记录当前c[i][j]的计值情况  1表示左上 2表示左 3表示上
int c[N][N];            //包含每一阶段LCS的长度
void print(int m, int n);

int main() {
    int i, j;

    for (i = 0; i <= n; i++)
        for (j = 0; j <= m; j++)
            c[i][j] = 0;

    for (i=1;i<=m;i++)                    //i表示行j表示列
        for (j = 1; j <= n; j++) {
            if (x[i] == y[j]) {
                c[i][j] = c[i - 1][j - 1] + 1;
                b[i][j] = 1;
            }
            else if (c[i][j-1] > c[i-1][j]) {
                c[i][j] = c[i][j-1];
                b[i][j] = 2;
            }
            else {
                c[i][j] = c[i - 1][j];
                b[i][j] = 3;
            }
        }

    for (i = 1; i <= m; i++) {
        for (j = 1; j <= n; j++)
            cout << b[i][j] << " ";
        cout << endl;
    }

    print(m, n);
    return 0;
}

void print(int m, int n) {
    if (b[m][n] == 1) {
        print(m - 1, n - 1);
        cout << x[m] << " ";
    }
    else if (b[m][n] == 2) {
        print(m, n - 1);
    }
    else if (b[m][n] == 3) {
        print(m - 1, n);
    }
    if (m == 0 || n == 0) return;
}

 

结果：